Upper limits on perturbations of nuclear decay rates induced by reactor electron antineutrinos

Applied Radiation and Isotopes 149 (2019) 182–199

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Upper limits on perturbations of nuclear decay rates induced by reactor electron antineutrinos

T

V.E. Barnesa,b, D.J. Bernsteina, C.D. Bryanc, N. Cinkoa, G.G. Deichertc, J.T. Gruenwalda,b, J.M. Heima, H.B. Kaplana, R. LaZura, D. Neffa, J.M. Nistora, N. Sahelijoa, E. Fischbacha,b,∗ a

Department of Physics & Astronomy, Purdue University, West Lafayette, IN, 47907, USA SNARE Inc., West Lafayette, IN, 47906, USA c High Flux Isotope Reactor (HFIR), Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN, 37831, USA b

HIGHLIGHTS

report the results of an experiment conducted near the High Flux Isotope Reactor of Oak Ridge National Laboratory, designed to address the question of • We whether a flux of reactor-generated electron antineutrinos can alter the rates of weak nuclear interaction induced decays of Mn-54, Na-22, and Co-60. experiment has small statistical errors but, when systematic uncertainties are included, has null results. • This greater than one part in 10 are excluded at 95% confidence level in beta decay and electron capture processes, in the presence of an antineutrino • Perturbations flux of 3 × 10 cm s . present experimental methods are applicable to a wide range of radionuclides. • The • Improved sensitivity in future experiments can be anticipated as we continue to better understand and reduce the dominant systematic uncertainties. 4

12

−2 −1

ARTICLE INFO

ABSTRACT

Keywords: Reactor physics Neutrino physics

We report the results of an experiment conducted near the High Flux Isotope Reactor of Oak Ridge National Laboratory, designed to address the question of whether a flux of reactor-generated electron antineutrinos ( ¯e ) can alter the rates of weak nuclear interaction induced decays of 54Mn, 22Na, and 60Co. This experiment has small statistical errors but, when systematic uncertainties are included, has null results. Perturbations greater than one part in 104 are excluded at 95% confidence level in ± decay and electron capture processes, in the presence of an antineutrino flux of 3 × 1012 cm−2s−1. The present experimental methods are applicable to a wide range of radionuclides. Improved sensitivity in future experiments can be anticipated as we continue to better understand and reduce the dominant systematic uncertainties.

1. Introduction Few issues frame the history of natural radioactivity as fundamentally as the question of whether radioactive decays are affected by their local environment. There is evidence to support this suggestion, including recent studies which have reported evidence of a solar influence on certain radioactive decay processes. This includes annual oscillations (Falkenberg, 2001; Alburger et al., 1986; Siegert et al., 1998; Fischbach et al., 2009, 2011a; Jenkins et al., 2009, 2010, 2011, 2012, 2013; Shnoll et al., 2000; Baurov et al., 2001; Ellis, 1990; Javorsek et al., 2009, 2010; Sturrock et al., 2010a, 2010b, 2011a, 2011b, 2012, 2013, 2014; O'Keefe et al., 2013) and indications of frequencies associated with solar rotation (Sturrock et al., 2010b, 2011b). On the other hand, ∗

Bergeson et al. (2017), Kossert and Nähle (Kossert and Nähle, 2015a), and Pommé et al. (Pommé et al., 2016) report negative results (see also Sturrock et al. (2018) for further discussion.) Additionally, a suggestion for a possible solar influence on nuclear decays comes from observations of short-term changes associated with solar storms (Jenkins and Fischbach, 2009; Mohsinally et al., 2016). Although some questions have been raised concerning the data supporting a solar influence (Cooper, 2009; Norman et al., 2009; Semkow et al., 2009; Kossert and Nähle, 2015b), they have been addressed in the literature (Jenkins et al., 2010; O'Keefe et al., 2013; Krause et al., 2012). As noted in Table 2 of Ref. (O'Keefe et al., 2013), the indications of a possible solar influence on radioactive decays come from experiments using a variety of detectors monitoring a number of different radionuclides. One

Corresponding author. Department of Physics & Astronomy, Purdue University, West Lafayette, IN, 47907, USA. E-mail address: [email protected] (E. Fischbach).

https://doi.org/10.1016/j.apradiso.2019.01.027 Received 28 March 2018; Received in revised form 13 October 2018; Accepted 30 January 2019 Available online 13 February 2019 0969-8043/ © 2019 Published by Elsevier Ltd.

Applied Radiation and Isotopes 149 (2019) 182–199

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hypothesis which could account for these observations is that they are due to the influence of solar neutrinos through some as yet unknown mechanism. This motivates the study of decay rates in the presence of more readily available electron antineutrinos (Lindstrom et al., 2010, 2011), including those produced by nuclear reactors. It is now well established that there exist three types of neutrinos denoted by e , µ , and their corresponding antiparticles ¯e , ¯µ , ¯ . Additional types of neutrinos or neutrino-like particles may exist such as sterile neutrinos (Palazzo, 2013) and neutrellos (Fischbach et al., 2011b). In what follows, we describe a reactor experiment aimed at studying whether nuclear decay rates are influenced by any light, neutral, and weakly interacting particle emitted by a reactor, including but not limited to the presumably dominant ¯e . We note that the limits presented below on perturbations induced by ¯e do not necessarily apply to the other neutrino flavors ( ¯µ, ¯ , …) which may have significantly different properties (e.g. magnetic moments). Our experiment was carried out at the 85 MW (thermal) High Flux Isotope Reactor (HFIR), located at Oak Ridge National Laboratory in Oak Ridge, Tennessee. This choice was motivated in part by the opportunity to position our experiment sufficiently close to the reactor core in order to achieve a ¯e flux comparable to or larger than the solar neutrino flux . Additionally, the routine reactor-refueling outages introduce a convenient step function in neutrino flux as the driving signal to generate the hypothetical perturbations. Planning for the experiment began in October 2013 and our first run began in March 2014. After initiating our reactor experiment at HFIR, we learned of reactor experiments by de Meijer, Blau, and Smit (de Meijer et al., 2011), and by de Meijer and Steyn (de Meijer and Steyn, 2014). The authors of the more recent paper indicate a positive effect for some of the isotopes studied. Phase I of this experiment, summarized in Appendix A, was an initial exploratory period which focused on understanding various systematic effects such as backgrounds and the sensitivity of our detectors to environmental conditions. Appendix A also describes many aspects of the detectors and sources, along with the radioactive decay chains of the sources used. The results presented here are derived from Phase II of this experiment. Due to its extended duration of 217 days, (with five reactor ON periods and more accurate temperature control), we achieved at least an order of magnitude better sensitivity in Phase II than in Phase I.

tube assembly relative to the enclosing aluminum can, we estimate displacement of the source relative to the NaI to be 1.95× 10 3 mm/K. At 4% per mm of source displacement, the resulting fractional change in solid angle subtended by the NaI is −7.8× 10 5 /K. Thermal swelling of the NaI increases the solid angle by 9.5× 10 5 /K. The resulting net fractional change in counting rate is 1.7× 10 5 /K, or 5.1× 10 7 per 0.3 K, which is negligible. Each of the eight detectors was connected to one of the two PCs at EF-3 via USB and programmed to run for one hour live-time intervals, where live-time denotes the real-time as measured in the laboratory minus the dead-time as reported by the digiBASE. Each detector thus runs for an interval greater than one hour, where the total real time is equal to the fixed one hour of live-time plus the variable amount of dead-time added by the detector. During this interval, the detector collects the output from the Multi-Channel Analyzer into a time integrated 1024bin histogram of energy. At the end of the time interval, information from this histogram is saved into two different files: one report file and one spectrum file. The spectrum file is simply a list of each of the 1024 bins and the counts recorded in each of those bins, while the report file gives a shorter summary of the data. In both files, basic information about the time interval is recorded, such as the date and time at which the measurement interval began, as well as both the real-time and livetime for the interval. Along with the detector hardware, ORTEC also provides the MAESTRO software in order to conveniently interact with their detectors. This software allows the user to set the high voltage, gain, gain locking, and other properties for each detector. In addition, during a measurement interval, the energy histogram (spectrum) is displayed on the screen optionally in either a linear or log scale. In order to make data acquisition and analysis easier, MAESTRO allows the user to set custom Regions of Interest (ROI) on the spectra for each detector. At the end of each time interval when the report files are published, the total counts for each ROI are summed over the specified energy range and reported. In addition to the integrated counts, MAESTRO fits a peak for the given ROI when a peak can be identified. MAESTRO reports a best fit for the centroid, full width at half maximum, and full width at fifth maximum, of the peak. The ORTEC digiBASEs provide optional gain locking and zero locking. The gain locking and zero locking algorithms each prompt the user to identify an ROI containing a peak to which the software will then lock. As a counting interval begins, the gain locking software continuously attempts to find a peak within the locked ROI (the user also sets the width, in bins, of the peak fitting region). If the ROI contains a peak, the algorithm will adjust the fine gain settings of the detector in order to align the measured peak center with the peak center set by the user when the gain was originally locked. In high statistics running with gain locking, the fitted peak location is stable to a small fraction of one bin. Zero locking ensures that the zero of the detector does not drift—if an identifiable peak exists. The combination of gain locking and zero locking makes it possible to essentially eliminate drifts in the gain and zero of the detectors, making measurements much more accurate in the long run.

2. Phase II experiment Phase II of our experiment, from which our results below are derived, took place between August 2014 and March 2015 at HFIR. Analysis of 152Eu and 241Am data has been omitted due to the relatively low energy of the chosen peaks, where the contribution from backgrounds is greater. This experiment included eight of the 2 inch NaI(Tl) scintillation detectors with digiBASEs described in Appendix A. Each detector—except for the two background detectors—had a radioactive source fixed securely to the front of the detector as in Appendix A. For Phase II, to accomodate the then upcoming PROSPECT neutrino experiment, the detectors were moved from site EF-4 to site EF-3 of the HFIR reactor, increasing the distance from the reactor core from 5.8 m to 6.6 m and reducing the ¯e flux to approximately 46 times the solar ν flux at Earth. A new lead cave was constructed that consisted of two levels with four detectors on each level. In addition to the sources in the original four bottom bays: Background Counter 1, 54Mn, 60Co, and 152 Eu, we added in the top bays a second background detector, a second 54 Mn detector, a 22Na detector, and an 241Am detector (data from this last detector were not analyzed because of low statistics and a very low energy spectrum). An insulating box with 2 inch thick polystyrene walls was built around the lead cave and maintained at a stable temperature of 20. 00 ± 0. 03 °C using a TECA thermo-electric heat exchanger with Watlow PID controller. A schematic representation of the detectors’ setup is shown in Table 6 in Appendix A. From the differential thermal expansion of the NaI-photomultiplier

3. Correcting for detector-induced rate-dependent distortions in the measured counting rate Pileup and dead-time are known problems in counting-detectors, which worsen with higher counting rates. The digiBASE corrects for the dead-time using a variant of the Gedcke-Hale algorithm. However, the MAESTRO/digiBASE system cannot correct for pileup effects. Pileup occurs when two photons which arrive in the detector close in time are not resolved, and the sum of their energies is registered as one event at a higher energy, and the other count is lost. The pileup effect is a ratedependent convolution of the energy spectrum with itself. Whether the pileup adds to, or subtracts from, a given ROI depends non-trivially on the shape of the spectrum. In all of the ROIs used in our present data, the appearance of pileup is similar to the effect of less than 2 μs excess 183

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Fig. 1. Exponentially detrended hourly counts vs. time, [and the full vertical fractional intervals for]: (a) 54Mn Det.2 [2.0× 10−3] (b) 54Mn Det.7 [1.7× 10−3] (c) 22 Na annihilation peak [2.0× 10−3] (d) 22Na gamma peak [4.7× 10−3] (e) 60Co low [1.4× 10−3] (f) 60Co high [1.8× 10−3]. The subtracted background amounts are plotted below the de-trended source plots, with identical vertical scales for comparison. The heavy black line is a 20-point moving average.

dead-time erroneously added per count. To achieve sensitivities better than one part in 104, we have chosen high overall counting rates up to 35 kHz, inducing dead-time as high as 13% and significant pileup. When counting a given radioactive sample for a significant fraction of one half-life, we observe a distortion in count rate relative to a pure exponential decay curve. The counting curve is steeper than exponential early in the measurement, and less steep than exponential late in the measurement. As noted in Appendix A, this distortion manifests itself in our data through half-life measurements that are systematically low (larger decay constants), and which steadily approach the published half-life values as the sample decays (as observed in Phase I of our experiment). These changes in decay constant are obviously purely instrumental and have nothing to do with putative variations in the actual decay constant. We emphasize that since the determination of precise decay constants was not the aim of this experiment, a trade-off was made. Higher counting rates were chosen to give better statistical accuracy in order to better detect steps in the counting rate. The distortion can be well modeled by a correction factor (1+ Ntot ) to be applied to the data to bring them into a pure exponential form. The parameter is typically 1.2–1.8 μs where Ntot is the overall counting rate into the electronics. This pileup correction factor is algebraically equivalent to what would happen if an excess dead-time of 1.2–1.8 μs were erroneously added to the run time for each count, in addition to approximately 4 μs of actual dead-time correctly assigned by the detector system. We emphasize that this form is a standard parameterization of the effects of pileup (Knoll, 2000), and that this does not mean that such excess deadtime is actually being added by the digiBASE. The exact counting rate distortion factor used in the “Global Fit” of Section IV is e Ctot (t ) , where Ctot (t ) Ntot (t ) × 3600s is the total number of counts in one hour. To a good approximation, the factor e Ctot is identical to (1 + Ntot ) (the exponent is typically 3% or less). and α differ by a factor of 3600 due to converting from counts per one-hour interval to Hz. Either the α or the version can of course be used in the exponential form. We choose the α version for convenience.

We emphasize that the rate-dependent distortion of the counting rate data is monotonic with time, and secular, i.e. varies smoothly over the duration of the measurements. With repeated ON/OFF cycles of the reactor, the hypothetical resulting multiple up and down steps in counting rate allow the extraction of the parameter ε, which is just the reactor ON vs. OFF fractional change in counting rate, with minimal effect from the rate-dependent distortion. The single parameter α, which is sufficient to achieve excellent distortion adjustment, brings the data into a smaller range of counting rates, allowing better visual inspection for residual systematic effects, as well as making any steps more prominent. 4. Determination of the parameter ε If the decay parameter, λ, changes in the presence of the reactor antineutrino flux, we expect different slopes of the decay curve between reactor-ON and reactor-OFF periods. Note that we measure the counting rate, which (if the solid angle subtended by the detector does not change) is proportional to dN / dt where N (t ) is the number of source nuclei as a function of time. If λ is stepwise constant, i.e. alternates for reactor OFF and ON, respectively, then the between values λ and counting rate is proportional to:

N (t ) =

dN d = (N0 e dt dt

t)

=

N0 e

t

(off)

(1)

At the moment when the reactor turns ON if λ changes to , N (t ) does not change instantaneously. Hence the step in λ must cause a step in the counting rate, and we would expect there to be a step in the counting rate each time there is a transition between ON and OFF or vice versa. This is a much more sensitive way of searching for changes in λ than through analysis of the slopes dN / dt themselves over time. To capture the entire set of effects with optimal use of the data, we perform a four-parameter Global Fit to the entire sequence of five ON and four OFF reactor periods. The function used is a stepwise sequence of exponential decays with alternating decay parameters λ and (1 + ) , 184

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Fig. 2. Exponentially detrended Monte Carlo data series reflecting the Gaussian statistics of (a) 54Mn [3× 107 hourly counts] (b) 60Co [1.2× 107 hourly counts] (c) 22 Na annih. [2.5× 107 hourly counts] (d) 22Na gamma [4.2× 106 hourly counts]. The total vertical fractional intervals are 4.3 × 10 4 , 6.7 × 10 4 , 4.8 × 10 4 , and 1.4 × 10 3 , respectively. The heavy black line is a 20-point moving average. ( on where off )/ off . We have systematically excluded 8 h of data following each change in reactor status (ON-OFF or OFF-ON) to account for the temporary time-dependences in ¯e flux as the reactor goes to full power, and for the time after fission stops until the radioactive decay heat “afterglow” becomes negligible compared to the 85 GW full power. The other two fitting parameters are C0 , the initial counts in one hour; and the distortion parameter α discussed in Section III. The exact formulas used are given in Appendix B.

origin. The total fractional spread is small, ranging from 4 to 10 parts in 10 4 . The effects of these systematics on ε will be quantified below, in three different ways. The results of the Global Fits are shown in Tables 1–3. The stated errors are purely statistical, and the 2 /dof are all somewhat larger than, but close to, 1. The two main 60Co peaks are fitted separately, as are the 22Na positron annihilation peak and the gamma peak from the daughter nuclide. The values of ε for the two 22Na peaks are in reasonable statistical agreement with each other, as are those for the two 60 Co peaks. There is a high correlation between λ and α for the two longer-lived radionuclides, which are relatively insensitive to α. Hence, for more robust fitting, we fix the values of α to be 3.35×10−10 ( = 1. 2 µs ) as determined with good agreement by the fits for the two 54 Mn detectors. With this choice, the half-lives of all four sources are fairly close to the published values, but differ from them (and in some cases, from each other) by several statistical standard deviations.

5. Analysis of results Our results are presented in Figs. 1–5. In Fig. 1 we show the data from both 54Mn detectors, along with the 22Na and 60Co detectors (two peaks each) detrended by pure exponentials using the fitted values of λ. These are simple 2-parameter fits with pileup and perturbation parameters forced to zero: α = 0 and ε = 0. The black curves are 20-point moving averages. The residual “U-shaped” distortions are seen in the two 54Mn plots. Given the longer half-lives of 22Na and 60Co, we expect such distortions to be less apparent since those counting rates have changed less during the experiment. ROI backgrounds based on Detector 1 or 8 measurements are subtracted on an hourly basis. Modest uncertainties in the background subtractions will be dealt with in our treatment of systematic uncertainties, below. The full background treatment is given in Appendix C. Although we acquired data from 152 Eu and 241Am, their quality was relatively poor and hence they were not analyzed. Generally, the moving averages wander more than expected from purely statistical fluctuations. To make this visually clear and to ”calibrate the eye”, Fig. 2 shows Monte Carlo simulated pure exponential decays for the three radionuclides, with Gaussian statistical fluctuations based on the hourly counts: 3× 107 (54Mn); 1.2× 107 (60Co); 2.5× 107 and 4.0× 106 for the 22Na annihilation and gamma peaks, respectively. The scales of the fluctuations in the simulations are much smaller than those in the measured data. Even after de-trending the α distortion, as seen in Fig. 3, these irregularities in the actual data are well above purely statistical, and hence must be systematic, and are of unknown

5.1. Systematic errors Where possible, we use the data to make estimates of systematic errors from unknown causes. We use three methods, described below. Additionally, we treat systematic errors from three known possible causes. If we fix the decay constants to the published values, as shown in Table 2, thus changing from a 4-parameter to a 3-parameter fit, the values of 2 /dof increase by less than 1% for 60Co and 22Na, and by 3.6% and 6.7% for the two 54Mn detectors. The values of α change modestly, but remain in the range of (3.3-5.5)×10−10. On the other hand, the values of ε change more substantially, and we take the changes in ε to be one of three estimates of the unknown systematic errors: (1) “Fit Change”. The other two quantitative estimates of unknown systematics are (2) the results of a “Shuffle Test” to be described below, and (3) the difference between ε values (“ ”) from the two 54 Mn detectors, (4.98±0.83)×10−5, and the two peaks each, in the 60Co and 22Na spectra, (1.31±1.25)×10−5 and (2.28±1.62)×10−5, respectively. However, for 22Na and 60Co are not statistically significant, and thus unlikely to represent systematic errors. Hence, to avoid 185

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Fig. 3. Exponentially- and α-detrended hourly counts vs. time, [and the full vertical fractional intervals for]: (a) 54Mn Det.2 [2.7× 10−3] (b) 54Mn Det.7 [2.3× 10−3] (c) 22 Na annih. [2.4× 10−3] (d) 22Na gamma [2.9× 10−3] (e) 60Co low [2.3× 10−3] (f) 60Co high [2.7× 10−3]. The subtracted background counts are plotted below the de-trended source plots, with identical vertical scales for comparison. The heavy black line is a 20-point moving average.

“double counting” in these two cases, we propagate the only for the comparison of the two 54Mn detectors. We note that for 54Mn is 6 standard deviations from zero and a clear indication of some (unknown) systematic effect(s). Three known systematic effects are: (1) due to the small uncertainties in the relative background levels in adjacent bays of the cave (see Appendix C). These, like the statistical errors, turn out to be negligible in quadrature with the three unknown-systematics estimates as we shall see below. (2) due to possible frequency shifts of the quartz crystal clock in the digiBASEs. A frequency shift would change the length of the live-time of a run, and hence the number of counts. Given the tight temperature control of the detectors, the manufacturer's specifications indicate better than 1 ppm frequency stability from thermal effects. Voltage dependence is better than 1 ppm for 5% variation of the voltage supplied to the oscillator circuit, which we take to be an upper limit on the stability of the USB voltage feeding the digiBASEs. Frequency shifts from aging of the quartz are less than 5 ppm in the first year, dominantly in the first two months. We take 5 ppm to be the upper limit on frequency shifts from all causes during the nine months duration of the data. Since this systematic error is both common to all detectors, and negligible compared to the dominant systematic errors, we omit it from the tables. (3) Gain locking, discussed in detail in Appendix D, by the MAESTRO/digiBASE system is almost perfect, but there are slight

gradual drifts seen in the fitted positions of the main peaks in the spectra, whereas the ROI boundaries are fixed. This can in principle cause shifts in the counting rate if the bin contents at the two edges of the ROI are not equal. However, the drift in counting rate is small, steady, and monotonic over the entire data-taking period. Hence it will have a completely negligible effect on the values of the fitted step-size parameter, ε, so we omit this from the subsequent analysis. 5.2. Shuffle test In order to further quantify the uncertainty of our results, we subject our data to a modified version of a standard Shuffle Test (Bahcall and Press, 1991; Sturrock et al., 2010c). We randomly shift the ON/OFF transition times from the actual values. Each transition time is shifted randomly with uniform weight in a restricted interval. The first interval is from the start of the entire data set to the midpoint between the first and second transition times; the second interval extends from this midpoint to the next one, etc. For each random choice of transition times, a Global Fit is performed. This is repeated 1000 times and the distribution of ε values is plotted. Since, in general, the shifted transition times treat a fraction of the ON states as OFF, and OFF as ON, any genuine reactor effect on the decay rate would tend to be diluted, driving the value of ε closer to zero, or even to the opposite sign if there 186

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value, comparable to the other radionuclides. For Detector 7 the σ from the Shuffle Test is 1.6× 10 5 , and in a significant number of cases ε is greater than the Globally Fitted value—again incompatible with a genuine reactor effect. It will be seen in the following section on error propagation that the shuffle estimates of uncertainty are dominant for all six measurements of ε. 5.3. Error propagation As discussed above, some of the systematic error estimates come from the differences in two values of ε: the “Fit Change” from the two alternative Global Fits, as shown in Table 3. Also shown in Table 3 is a discrepancy in the measured values of 54Mn ε between Detectors 2 and 7. This unknown systematic error, presumed random, is estimated using the “scatter” of two values. We apply the formula (Wikipedia, 2016) for the corrected and unbiased estimator of σ from two samples:

=

s , C4 (N )

(2)

with

s=

(x i N

x¯) 2 and C4 (N ) = 1

() N 2

( ) N

1

2

2 N

1

. (3)

It follows from Eq. (3) that

=

|x1 x2 | 1.128

(4)

for N = 2 . This gives = | Det7 from the Det2 |/1. 128 = 4.41 × 10 two 54Mn detectors. The values of ε from the six analyzed peaks are given in Table 3, together with their statistical errors and three of the four types of systematic error discussed above. The known systematic clock frequency stability uncertainty of ± 5 ppm, which is common to all detectors, is negligible and is not included in the table. Also shown are the statistically weighted averages of the two ε values for each radionuclide. The background systematic errors are propagated in quadrature for each radionuclide. The differences in ε for 22Na and 60Co are not statistically significant, which is not surprising since the same detector is measuring both peaks for the radionuclide. Note that the Shuffle Test systematic errors are quite similar within a given detector. The Fit Change estimates for 22Na and 60Co are small and will contribute little to the overall uncertainty. The 1275 keV Na data also have small statistical weight relative to the more abundant positron annihilation peak. Since some of the unknown systematic errors are probably common to a given detector, we use the mean of the two Shuffle uncertainties in the summary lines for 22Na and 60Co in Table 3, and similarly for the Fit Change column. Further justification for this choice can be seen in parts (c),(d) of Fig. 3: the long-term features of the 22Na data for the two peaks are similar, showing some degree of correlation. In parts (e),(f) of this figure, for the two 60Co peaks, the shorter term fluctuation patterns appear rather similar, again showing some degree of correlation. The case is not so clear for 54Mn, since two different detectors are involved, but the values of the uncertainties in each of the two columns are nearly equal. Moreover, the 54Mn parts of the figure, (a),(b) show some degree of correlation, with an initial drop followed by a dip at around day 70 in both detectors (the dip at around day 70 is also present for the Co plots (e),(f)). In any case, we conservatively propagate the Fit Change and Shuffle errors for 54Mn in quadrature. 5

Fig. 4. Distributions of ε from Global Fits to 1000 Monte Carlo random shuffles of the reactor transition times for two simulated data sets: (a) ε = 0 (b) ε =10 4 . Both use typical 54Mn counting rates [3 × 107 hourly counts]. The Globally Fitted values of ε are shown with arrows on the x-axis, which is the ε -axis. The y-axis is in arbitrary units.

is a preponderance of wrong assignments of both reactor states. In general, one would not expect the magnitude of ε from a genuine reactor effect to be increased by the shuffle; N Gaussian statistics alone cannot drive values of ε larger than the best fit value in a shuffle test. To demonstrate this, two simulated decay sets were generated with a value of λ equal to that of 54Mn, one with no steps and one with = 1 × 10 5 . The statistics were determined by Gaussianly distributing the counts about the exponential, with N statistics and N0 = 3 × 107 counts per hour. The resulting data streams were then processed by the Global Fitting procedure described above. The dilution of ε (i.e. suppression) by incorrect transition times is clearly seen in Fig. 4; for the non-zero-ε case, ε is never more than the input value (the no-step sequence has a “shuffle sigma” much smaller than all the others, reflecting the absence of systematic errors). Fig. 5 shows the frequency distributions of ε for the three radionuclides. All six distributions are reasonably fitted by Gaussians. For the two 60Co peaks, the values of ε are widely distributed on either side of the (small) Globally Fitted values, with standard deviations (σ) of 3.6× 10 5 and 4.2× 10 5 . We consider these deviations as estimates of the effects of the visible systematic fluctuations in the detrended data. Note that these standard deviations are considerably larger than the Globally Fitted statistical uncertainties. The 22Na shuffle distributions, in more than half of the cases, increase the values of ε, clearly impossible for a genuine reactor effect. The Gaussian σ′s are 6.9× 10 5 and 7.9× 10 5 , again considerably larger than the Globally Fitted statistical errors. For the 54Mn in Detector 2, the value of σ is 3.0× 10 5 and many values of ε are greater than the Globally Fitted

6. Conclusions Table 4 summarizes the three values of ε from the three radionuclides. The statistical errors and the small systematic errors in relative bay-to-bay background levels are both almost insignificant when added in quadrature to each of the estimates of unknown systematic 187

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Fig. 5. Distributions of ε from Global Fits to 1000 Monte Carlo random shuffles of the reactor transition times for: (a) 54Mn Det.2 (b) 54Mn Det.7 (c) 22 Na annih. (d) 22 Na gamma (e) 60Co low (f) 60Co high.

errors for each radionuclide. Note that because there is no significant statistical discrepancy among detectors, the estimates for 22Na 60 and Co are not used, to avoid “double counting”. We quote the final results for ε as two-sided 95% C.L. “outer limits” (mean value ± 2× overall σ). In summary, while this experiment is quite sensitive statistically, given the estimated systematic errors the 95% CL outer limits are plus or minus one or two parts in 104 on perturbations in ± decay (or electron capture) processes in the presence of an antineutrino flux of 3×1012 cm−2s−1. Our 10−4 exclusion level is roughly comparable to that of de Meijer and Steyn (de Meijer and Steyn, 2014), who find for 22 Na a relative change between reactor-ON and reactor-OFF of

( 0.51 ± 0.11)× 10 4 (which translates to outer limits [-0.73, −0.29]× 10 4 ), but do not exclude possible systematic errors. In a more recent paper, de Meijer et al. (de Meijer et al., 2016) find a much larger non-zero value, ( 3. 04 ± 0. 26(stat) ± 0. 03(syst)) × 10 4 , which is in contradiction to our present outer limits for 22Na [ −1.12× 10 4 , 1.79× 10 4 ] (and to their original result). A non-null measurement is outside the Standard Model of particles and forces, and calls for further measurements of 22Na decay. If we define an effective “cross section” e to characterize the change in λ induced by a change in anti/ , then we find for our experiment e neutrino flux, e = 9× 10 25 cm2, which compares to e =(2.9 ± 0.6)× 10 25 cm2 [or (1.7 ± 0.15)× 10 24 cm2 ] cited in the first [or second] papers by de

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Table 1 Global fit results. radionuclide 54

Mn

Feature

λ (days−1)

Det. 2

2.23175× 10

3

2.23392× 10

3

7.29416× 10

4

7.39604× 10

4

3.66119× 10

4

3.67259× 10

4

±

stat

a

Det. 7

22

Na

511 keV 1275 keV

60

Co

1173 keV 1333 keV

a

7.5× 10

7

7.0× 10

7

4.9× 10

8

1.2× 10

7

6.7× 10

8

7.4× 10

8

C0

α (s)

2.92× 107

3.224× 10

10

3.472× 10

10

1.2× 10 4

3.45× 107 1.3× 10 4

2.47× 107

4.4× 10

12

3.4× 10

12 10

4.13× 106

3.35× 10 Fixed

10

1.32× 107

3.35× 10 Fixed

10

3.35× 10 Fixed

10

6.5× 101

1.2× 10 2

1.09× 107 1.1× 10 2

−1.21× 10 6.2× 10

Published (d)

1.295

310.58

312

1.5× 10

5

1.150

310.28

1.490

950.28

1.143

937.19

1.166

1893.23

1.116

1887.35

6

2.96× 10

6.1× 10 6.3× 10

5

6

4.05 × 10 5.7× 10

3.35× 10 Fixed

1.6× 10 2

Half-life (d)

2 /dof

ε

5

6 5 5

−1.26× 10

8.3× 10

6

9.3× 10

6

1.74× 10

5

7

0.07 0.07

0.04

949.7

0.11

0.24

1924.9

0.26

Statistical errors are given below fitted values in every row.

Table 2 Global Fit Results With λ Fixed to Published Value. radionuclide 54

Mn

λ (days−1)

Feature

C0

Det. 2

2.90× 107

±

stat

a

Det. 7

2.221× 10 Fixed

3

2.221× 10 Fixed

3

3.601× 10 Fixed

4

4.07× 106

3.601× 10 Fixed

4

1.30× 107

7.299× 10 Fixed

4

7.299× 10 Fixed

4

6.5×

10 2

3.43× 107 6.9× 10 2

22

Na

511 keV 1275 keV

2.47× 107 1.6× 103

6.5× 10 2

60

Co

1173 keV 1333 keV

2.3× 103

1.07× 107 2.1× 103

a

α (s) 3.858× 10

10

4.102× 10

10

3.265× 10

10

5.249× 10

10

5.051× 10

10

5.371× 10

10

2.9× 10

13

2.2× 10

13

9.6× 10

13

2.3× 10

12

1.9× 10

12

2.1× 10

12

Published Half-life

2 /dof

ε −2.23× 10 6.1× 10

6

5.6× 10

6

2.75× 10

3.05× 10

5

5

1.227

5

1.494

6.1× 10 6 5.33× 10 5 1.5× 10

1.341

312 d

2.60 a

1.127

5

−1.24× 10 8.3× 10

6

9.4× 10

6

−6.82× 10

5

1.161

7

1.112

5.27 a

Statistical errors are given below fitted values in every row.

Table 3 Epsilons with all errors. statistical uncertainties

systematic uncertainties

radionuclide

Feature

ε

54

Det. 2

−2.23× 10

Mn

Det. 7

Average 22

Na

511 keV

1275 keV Average

60

Co

1173 keV

1333 keV Average

2.75× 10

± stat.

6

3.05× 10

5

3.38× 10

6.82× 10

5 5

7

−7.24× 10

6

4.1× 10

6

6.1× 10 1.5× 10

5

−1.24× 10

6.1× 10 5.6× 10

5

4.80× 10

5.33× 10

5

Bkgd.

6

6

6 5

5.6× 10

6

8.3× 10

6

6.2× 10

6

9.4× 10

6

2.6× 10

6

Fit Change

Shuffle

9.1× 10

4.04× 10

1.2× 10

6

3.09× 10

5

2.3× 10

6

3.5× 10

6

1.5× 10

5

5.08× 10

5

4.2× 10

6

7.9× 10

7

6.72× 10

5

1.0× 10

5

3.0× 10

6

4.4× 10

6

9.0× 10

3.3× 10

6

6

5

7.61× 10

5

8.6× 10

6

4.7× 10

6

7.43× 10

5

1.9× 10

7

3.61× 10

5

7.6× 10 4.7× 10

7 7

4.21× 10 3.90× 10

5

5 5

In the statistical uncertainties section, a weighted average is given below the ε and ± stat. columns for each radionuclide. In the corresponding rows of the systematic uncertainties section, the errors are summed in quadrature for each radionuclide.

Meijer et al. If we assume that the interaction strength of ¯e with radioactive radionuclides is the same as that of e , then our upper limit excludes e as the dominant source of the O (10 3) effects reported in some of the original papers (Falkenberg, 2001; Alburger et al., 1986;

Siegert et al., 1998; Fischbach et al., 2009, 2011a; Jenkins et al., 2009, 2010, 2011, 2012, 2013; Shnoll et al., 2000; Baurov et al., 2001; Ellis, 1990; Javorsek et al., 2009, 2010; Sturrock et al., 2010a, 2010b, 2011a, 2011b, 2012, 2013, 2014; O'Keefe et al., 2013; Jenkins and Fischbach,

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and smaller backgrounds, are being planned. Given the small statistical uncertainties of the present method, an improvement in sensitivity can be anticipated as we continue to reduce the dominant systematic uncertainties.

Table 4 Final epsilons. radionuclide 54 22 60

Mn Na Co

ε 4.80× 10 3.38× 10

6

95% LL

6.91× 10

−1.33× 10

4

−8.69× 10

5

7.27× 10

5

−7.24× 10

Total error

6

3.98× 10

5 5 5

−1.12× 10

95% UL

4

1.43× 10

4

7.24× 10

5

1.79× 10

4

Acknowledgments We wish to thank J. J. Coy, R. de Meijer, S. Fancher, J. Herczeg, G. W. Hitt, J. H. Jenkins, D. Koltick, M. Pattermann, P.A. Sturrock, and T. Ward for helpful communications. We are deeply indebted to the staff of Oak Ridge National Laboratory for their assistance in carrying out this experiment. This study was funded by the Office of Nuclear Energy, U.S. Department of Energy under contract number DEDT0004091.001b.

2009; Mohsinally et al., 2016). However, as noted in the Introduction, our results do not impose any constraints on the coupling strengths of other neutrino flavors, which are present in both the solar neutrino flux and the cosmic neutrino background, but are not significantly present 6 m from the HFIR reactor core. The present experimental methods are applicable to a wide variety of radioactive radionuclides. Further measurements, with even tighter control of environmental variables Appendix A. Phase I Experiment

We summarize in this Appendix the features of the Phase I experiment which also apply to the Phase II experiment from which our final results were derived. Table 5 presents details of the decay data of sources used in this experiment. Data acquisition in Phase I commenced on 15 March 2014 at 04:24 with the reactor ON and continued through the reactor shutdown (23 March 2014 at 05:23) until 30 March 2014. This provided for an ON/OFF comparison of the decay rates of the radioactive radionuclides that were studied. In Phase I the decay rates of three radioactive radionuclides were studied: 54Mn which decays by electron capture (EC), 60Co which decays by beta-emission ( ), and 152Eu which has significant branching through both EC (72.10% ) and decay (27.90% ) modes. The nuclides were chosen, in part, due to indications in earlier experiments (Falkenberg, 2001; Alburger et al., 1986; Siegert et al., 1998; Fischbach et al., 2009, 2011a; Jenkins et al., 2009, 2010, 2011, 2012, 2013; Shnoll et al., 2000; Baurov et al., 2001; Ellis, 1990; Javorsek et al., 2009, 2010; Sturrock et al., 2010a, 2010b, 2011a, 2011b, 2012, 2013, 2014; O'Keefe et al., 2013) that each had exhibited a time variation in its decay constant, possibly due to solar neutrinos. In Phase II, described in the body of the text, we added detectors with 22Na and a second 54Mn source. Table 5

Decay Data of Sources Used in This Experiment. The notation (g.s.) describes a transition to the ground state of the daughter nucleus. 54 * 54 Cr + e (100% )↪ Cr54 24 (g. s.) + γ(834.8 keV) 25 Mn + e (EC) 22 22 + Na e + e (90% ) ↪ e+e (511 keV) 10 Ne + 11 22 Ne∗ + e (10% ) ↪ 22 10 Ne(g.s.) + γ(1274.5 keV) 11Na + e (EC) 60 Ni∗ + e− + ¯e ( 100% ) ↪ 60 28 Ni (g.s.) + γ(1173.3 keV) + 27Co 152 Sm∗ + e (73% ) ↪ 152 62Sm(g.s.) + γ(122 keV) 63Eu + e (EC) 152 Gd∗ + e + ¯e (27% ) ↪ 152 64Gd(g.s.) + γ(779 keV) 63Eu

T1/2 = 312 d T1/2 = 2.60 a = 949.7 d γ(1332.5 keV)

T1/2 = 5.27 a = 1924.9 d T1/2 = 13.54 a = 4945 d

Further motivation for the choice of 54Mn comes from an apparent correlation between changes in the 54Mn decay rate and the solar storm of 13 December 2006 (Jenkins and Fischbach, 2009) and subsequent storms (Mohsinally et al., 2016). This radionuclide is also of interest since its dominant decay mode is electron capture and hence allows a comparison to the radionuclide 60Co, which is a pure decay. Cobalt-60, in turn, was selected on the basis of the observation by Parkhomov of an annual variation in its decay (Parkhomov, 2011). Finally, the choice of 152Eu was dictated by the fact that this radionuclide decays via both EC and modes. Moreover, the data presented by Seigert et al. (Siegert et al., 1998) indicate periodicity in the intensity (count rate) of the 1408 keV γ emitted in the EC process. This particular observation is especially interesting since the periodic signal, obtained using a Ge(Li) detector, was observed to be 180 days out of phase with the data taken by the same group on 226Ra and its daughters using a 4 γ-ionization chamber (Siegert et al., 1998). Additionally, radionuclides were preferred which decayed to the excited state of the daughter nucleus. This would ensure that the decay of the parent could eventually be recorded by the photons emitted in the nuclear deexcitation of the daughter to its ground state. Since such a decay produces a sharp peak at a well-defined energy, this allowed us to focus on a relatively narrow region-of-interest (ROI) in the γ-spectrum whose location in a Multi-Channel Analyzer (MCA) could be identified and controlled. Among radionuclides whose decays suggest interesting effects, 3H, 32Si, and 36Cl are decays with no photons and thus not suited to be detected by our NaI crystal scintillators. These considerations led to our selection of 54Mn, 60Co, and 152Eu in Phase I, joined by 22Na in Phase II. Particular attention was devoted to 54Mn (T1/2 = 312d) with which we had the most extensive experience from our previous experiments at Purdue. 54Mn decays via electron capture and is detected via the chain exhibited in Table 5. We note in passing that our choices led to a set of radionuclides with a broad range of half-lives: 54Mn (312 d), 22Na (2.60 a), 60Co (5.27 a), 152Eu (13.54 a). All published half-lives are taken from Ref. (Nuclides and Isotopes, 2002). The sources have activities of several μCi (1 Ci = 3.7×1010 decays per second) and give counting rates of order 20–35 kHz, which induce detector dead-times in the range 10%–13%. The sources were encapsulated in standard 1-inch diameter plastic discs. In Phase I of this experiment the apparatus consisted of four detectors, including one with no source mounted as a control and to measure background counting rates. The detectors were St. Gobain/BICRON 2 inch NaI(Tl) crystal plus photomultiplier, sealed assemblies, in 2.25 inch diameter cylindrical aluminum cans. Each detector was coupled to a digiBASE (ORTEC), an electronically gain-locked PMT base which includes a high voltage supply, preamplifier, and multichannel analyzer. Dead-time in the system was corrected by implementation of a variant of the Gedcke-Hale live-time clock, which extended the running time of a measurement cycle until the requested live-time was achieved. Data acquisition across all detectors was 190

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performed with software MAESTRO (ORTEC) running on one central personal computer, connected to the PMT bases via USB. The source discs were each mounted on a triangular metal plate affixed to three thin standoffs matching the periphery of the front end of the detector can. These standoffs were then affixed to the edge of the front face of the can. The objective was to avoid motion of the source by possible barometric flexing of the front disc of the sealed can. (This had been seen to happen if the source is mounted directly to the center of the front disc with small, concomitant but significant fluctuations in counting rate.) The objective of the experiment was to be sensitive to fluctuations in counting rates fractionally smaller than 10−3. This requires very stable geometry of the source position relative to the detector: a simple geometrical calculation shows that a point-like source located 6 mm from a 50 mm diameter, 50 mm long crystal (typical of our assemblies), and displaced 1 mm towards or away from the crystal, sees a change in the subtended solid angle of ± 4.8% at the front face of the crystal, and ± 3.14% at the back face of the crystal. This represents an average of ± 4% per 1 mm motion, or as a useful mnemonic, 1 part per thousand per 0.001 inches (25 μm) of motion. Background suppression was achieved by surrounding each detector by at least 4 inches (10 cm) of lead. Moreover, the detectors were separated from one another by 4 inches of lead to mitigate cross-talk in a structure, referred to as the cave, with four bays (see Fig. 6 for details). Altogether, approximately 1.8 metric tons of lead were required, using 150 standard 2×4×8 inch3 lead bricks.

Fig. 6. (a) Schematic drawing of the layout of each detector bay within the lead cave. Hashing denotes lead bricks and open regions denote spaces for the NaI detectors. Dimensions are given in inches. (b) Diagram of the lead cave in Phase I. The large block under the cave represents the floor.

With the reactor ON, backgrounds outside the cave were typically a few thousand counts per second (cps). The lead shielding was effective in reducing the background by nearly 3 orders of magnitude, and we conservatively mounted the background detector in the highest-count bay (bay # 1). The gain of the background counter was set lower than any of the other detectors, so that it was sensitive to any gamma (γ) energy that would arise from any of our radionuclides. The counting rate refers to the entire spectral range of the background counter, whereas only portions of the background will fall in the regions of interest (ROIs) used for counting. The total counting rates from backgrounds inside the cave were small, of order 10 3 of the counting rates from the sources. Hence in Phase I, 191

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background estimates were not subtracted from the source counts, although they were in Phase II, from which our final results were obtained. Moreover, fluctuations in the interior background rates were less than 20% of the average background level, and were believed to be associated with the intermittent operation of a neutron beam line passing one floor below in the reactor building. The lead cave and the detector array were situated 5.83 m from the HFIR reactor core at site EF-4, directly along one of the reactor-core center lines, 4 m higher than the core and 4.27 m away laterally. The core is a cylinder 20 cm in diameter and 40 cm in height, which we treat approximately as point-like for flux calculations. Calculations by our group and others (Huber, 2011) of the total ¯e flux from highly enriched uranium reactors give a ¯e flux at 5.8 m from HFIR, at 85 MW thermal output, of 3.8×1012 cm−2 s−1, which is 58 times larger than the solar ν flux at Earth, 6.5×1010 cm−2 s−1, and 830 times larger than the 7% annual variation in the solar ν flux due to the Earth's orbital eccentricity. Since the power of the HFIR reactor is known to be constant, it is presumed that the ¯e flux is as well. As noted above, primary data acquisition started on 15 March 2014 at 04:24 EDST with the reactor already ON, and consisted of a continuous stream of 30 min (live-time) cycles. Each cycle produced a γ energy spectrum, and a table of counts from each of a set of selected ROIs (i.e. groups of bins in the energy spectrum). The reactor ran at approximately 85 MW thermal power (see Fig. 7) until it was shut down at 06:00 on 23 March 2014. Thermal power dropped to 0.2 MW in the succeeding three hours and then effectively to zero, presumably reflecting the initial part of the afterglow arising from short-lived fission products. Data acquisition then continued in the OFF period until 30 March 2014.

Fig. 7. HFIR thermal power (MW) output for a 10 day test run. The HFIR reactor was shut down for routine maintenance on 23 March 2014, at 06:00, which corresponds to day 8.25 on the above graph.

Residual ¯e flux from the spent core is expected to be below 1%. Although multiple spent cores are stored at the other end of the reactor pool in which the reactor operates, they are at distances from our detectors several times the distance of the operating reactor. The most recently extracted core emits copious Cherenkov radiation as seen from the observation gallery, however the next most recent core shines only dimly. The ages of the spent cores increase in increments of roughly two months. Suppression of ¯e flux due to decay time and distance were estimated to outweigh the increase in ¯e flux due to the number of spent cores stored in the pool, as seen at our detectors. Temperature control of the detector-source assembly is very important. Differential thermal expansion of the NaI(Tl) crystal mounted onto a glass PMT envelope versus the surrounding aluminum can will partly, but not necessarily, completely cancel shifts of the front end of the can relative to the crystal. Sodium iodide has a larger expansion coefficient, and glass has a lower coefficient, compared to aluminum. Also, expansion of the NaI(Tl) crystal will increase the solid angle subtended. The temperature at the experimental location was climate controlled within approximately 2 °C and, as monitored at one of the detectors inside the lead cave, remained within a 0.2 °C range for most of the period while the reactor was ON. This climate control in the hall was unexpectedly discontinued (due to HVAC failure) when the reactor was shut down, following which the temperature measured by the sensor located at bay # 4 in the lead cave rose by 6 °C from day 9 to day 15 in two stages, and then started to drop. This motivated incorporation of an independent temperature control for the Phase II experiment. We conclude this section with a brief summary of the Phase I results as they relate to the subsequent Phase II experiments. A more complete description of the Phase I data can be found in (Barnes et al., 2016). In addition to the importance of independent temperature control noted above, the Phase I data highlighted the importance of dead-time and pileup effects in our detectors. Specifically, the 312 d half-life of 54Mn was sufficiently short that the ∼10% change in counting rate over the course of a ∼1 month run produced changes in dead-time/pileup corrections that had to be modeled more carefully at the sensitivity levels we were aiming to achieve. The specific indication for the more detailed modeling of dead-time and pileup, to be described below, was the observation that the Phase I data did not reproduce the accepted 312 d 54Mn half-life when the reactor was in the OFF mode, as we had expected. The half-lives and decay modes of the nuclides studied in both Phase I and Phase II are presented in Table 5. We do not include 241Am due to the very low energy of the relevant gamma peaks, where backgrounds are large. The primary signal for an ON/OFF antineutrino effect at HFIR in Phase I would have been a systematic difference between the 54Mn half-life (and others) associated with the reactor ON compared to reactor OFF. However, necessity for the aforementioned pileup/dead-time corrections led to implementation of a superior criterion for an ON/OFF signal: the presence of a step-function change in the 54Mn (and other) decay rates associated with an ON/OFF or OFF/ON transition in the HFIR power. The magnitude of this change, reflected by the parameter ε introduced below, is relatively insensitive to the gradual changes that arise from the long term secular changes in pileup/dead-time corrections due to the decay of the 54Mn sample. Table 6

Detector Layout Detector 5 241Am Detector 1 Background

Detector 6 Detector 2

22 54

Na Mn

Detector 7 Detector 3

192

54 60

Mn Co

Detector 8 Background Detector 4 152Eu

Top Layer Bottom Layer

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Fig. 8. Energy spectra with chosen ROIs for: (a) 22Na (b) 54Mn (c) 60Co. The x axis is energy channel number in bins 1 through 1024; the y axis is counts per channel on a linear scale.

Appendix B. The Global Fitting Formalism The Global Fitting formulas described in Section V use just four parameters: C0 (the initial counts in one hour); the decay constant, 0 off ; ( on off )/ off ; and the parameter α used in the rate-dependent distortion factor described in Section III. We measure the counting rates in the form of the dimensionless number of counts in each one hour of live time. To illustrate the functional form of the Global Fit, assume that an experiment began in an OFF period and lasted for a time T1, followed by an ON period which lasted for a time T1 . Then at the end of the first ON and OFF periods we have for OFF1

N (T1) = N0 e

(B1)

0 T1

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and for

ON1, 0 (1 + )(t T1)

N (t ) = N (T1 ) e

= N0 e

0 [(T1+ T1 ) + T1 ]

N (T1 + T1 ) = N0 e

(B2)

0 [t + (t T1)]

(B3)

.

The first term of the exponential in Eq. (B3) gives the surviving number of atoms after a cumulative time (T1 + T1 ) starting from N0 , assuming no influence from reactor antineutrinos. For > 0 assumed, the dependent contribution then gives an additional loss during the time T 1 due to the excess in the decay constant, 0 . The results in Eqs.(B1-B3) can be generalized in an obvious way: the number of surviving atoms N (t ) after a cumulative elapsed time t is given by

N (t ) = N0 e

0 t+

Ti

(B4)

i

In Eq. (B4), i Ti extends over only ON periods Ti , during which it is assumed that any additional reactor-ON contributions enter with the same factor ε. For the HFIR reactor at Oak Ridge this assumption is justified given that during each ON period the reactor runs at the same 85 MW rate using the same fuel composition. What is actually measured is the counting rate, or its proxy, the hourly count total C (t ) . Incorporating the counting rate dependent distortion factor described in Section III, e C (t ) gives for OFF periods:

C (t ) = C0 e and for

0 t+

Ti + C (t )

(B5)

i

ON

periods:

C (t ) = C0 (1 + ) e Once again,

0 t+

Ti + C (t ) i

(B6)

.

Ti is the sum of all

ON

time intervals up to the data point at time t.

Appendix C. Background Subtractions As can be seen in Figs. 1 and 3, the backgrounds from a variety of sources are small and steady in the reactor-OFF periods. However, backgrounds during reactor-ON periods are larger and highly irregular due to several intermittently-operated neutron beam lines one floor below the detectors. The general effect of such backgrounds, if not dealt with, could mimic an increased decay rate during reactor-ON periods, and could thus generate false steps and a spurious positive value of ε. Although background effects at HFIR and other high power research reactors have been studied previously by Ashenfelter et al. (Ashenfelter et al., 2016), we felt that it was important to make detailed measurements at the specific sites of our detectors, given that backgrounds can vary from place to place at a reactor such as HFIR. Two counters, with no installed sources, were located in bays #1 and #8 on the lower and upper levels, respectively, of the cave—as in Table 6. We use the background information on an hour-by-hour basis. At the start of Phase II, which was during a reactor-ON period, each of the two background counters was placed in each of the eight bays of the lead “cave” to measure the relative background levels. The results, as measured by Detector 8, are shown in Table 7, where the background-level scale factors of the top row are relative to bay #8 and the bottom row scale factors are relative to bay #1. These original calibration runs had five minute live times, and in Detector 1 typically had approximately 4800 counts in top-row bays and 3500 counts in bottom-row bays. The resulting statistical uncertainties in Table 7 are 2.0% for the top row and 2.4% for the bottom row. These uncertainties lead to one type of systematic error on ε, shown in Table 3, which is quantified by varying the amount of background subtracted for the Global Fit analysis. The relative gains of all eight detectors are well measured and any gain-induced uncertainties will contribute negligibly to the sizes of the background subtractions. Table 7

Ratio of Initial Background Counts Relative to Detector 1. See text for further discussion. Det5 Am: 0.917 Det1 Bkg: 1.00001 a b

Det6 Na: 0.871b Det2 Mn: 0.895

Det1 Bkg: 1.0000a Det4 Eu: 1.075

Det7 Mn: 0.951 Det3 Co: 0.936

± 0.020 ± 0.024

Top row ratios are relative to Bay 8 and bottom row ratios are relative to Bay 1. For the Na annih. peak, background subtraction is done with Det. 8 data, and the initial ratio relative to Det. 8 is 0.911.

Table 8

Gains relative to Detector 1 (2.646 keV/bin). See text for further discussion. Det5 Am: 9.093 Det1 Bkg: 1.000

Det6 Na: 1.326 Det2 Mn: 1.478

Det7 Mn: 2.412 Det3 Co: 0.979

Det8 Bkg: 4.260 Det4 Eu: 1.042

The lower four counters are better shielded than the upper-level counters, by two lead layers instead of one. Also, central bays are more shielded than side bays. In general we expect the central bays to have somewhat smaller background counting rates than the side bays, and the top row of bays generally to have significantly larger background levels than the bottom row. The gain of Detector 1 is set near or lower than any of the other gains, to cover all background energies that could lie at one of the source detectors’ main gamma peaks. The gain of Detector 8 is larger than any of the other gains (4.26 times the gain of Detector 1), and hence Detector 8 does not cover the energy range of almost any of the peaks of interest in counters with radioactive sources (with the exception of the 22Na positron annihilation peak). Detector 8 can be used directly for the 22Na annihilation peak. For the 22Na gamma peak and the Detector 7 54Mn peak, we can approximately recover the missing Detector 8 information by using 194

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the Detector 1 information, scaled up by the ratio of counts in an overlap region defined by bins 860 to 1023 in Detector 8. This maps approximately onto bins 202 through 240 of the Detector 1 spectrum. Since the gains of the detectors are all different, we must of course map a given ROI onto the corresponding energy range in the relevant background counter. Additionally one must also take careful account of fractional bin contents. We can justify the use of Detector 1 data to replace missing Detector 8 data as follows: The Detector 1 spectra measured in bays 1 through 4 (Bottom) are summed, and similarly for bays 5 through 8 (Top), and are shown in Fig. 9. The spectral shapes are very similar, both in the scaling region and also in all energy regions of interest, as is seen in the Top/Bottom ratio plot of this figure.

Fig. 9. Various sums of reactor-ON spectra from 5 min initial Phase II background runs with Detector 1 in all eight bays of the the cave: (a) Sum of top bays (b) Sum of bottom bays (c) Ratio of top sum to bottom sum. Energy regions of interest and the Det1-Det8 scaling overlap region are shown as horizontal bars. The heavy black line is a 20-point. moving average.

From the main running periods, we have much higher background statistics by summing spectra from several days of running, and this allows us to study the reactor-OFF backgrounds. Such summed background spectra for both detectors for ON and OFF are shown in Fig. 10. During ON periods, the spectrum is rather smoothly decreasing after the last peak (which is somewhat below bin 200 in Detector 1). The chosen overlap scaling region is 195

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shown as a horizontal red bar, as are the various energy regions of interest. The OFF period background levels are some five times lower than for the ON period, and the spectrum falls off more quickly and has very little of the structure just below bin 200 in Detector 1. Hence the scaling/splicing procedure should work equally well, or better during OFF periods.

Fig. 10. 3-day sums of background spectra for reactor-ON and -OFF with Detector 1 in bay 1 and Detector 8 in bay 8: (a) Det. 1 ON (b) Det. 1 OFF (c) Det. 8 ON (d) Det. 8 OFF. Energy regions of interest and the Det1-Det8 scaling overlap region are shown as horizontal bars. 196

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The Detector 1 gain locking was set for a peak in bin 54, which is present when the reactor is ON. This peak is absent when the reactor is OFF. In the absence of the chosen peak, the gain locking algorithm mistakenly recognizes a peak in bin 13, and it very slowly and steadily (due to the very low statistics) increases the gain. This can be seen in Fig. 11, where the gain increases by some 12% over the first 32-day OFF period. When the reactor turns ON, the gain is restored fairly quickly (due to the five times higher counting rate). This gain drift is easily corrected for in the subsequent analysis by rescaling the energy spectrum after the fact using the observed gains. The Detector 8 gain locking worked as intended, and no correction was needed. The counters run asynchronously with different dead-times (and negligible dead-time for the background counters.) Thus more than a single onehour background count period is matched to a given source count period. Background information is taken from these overlapping periods in such a way that only 60 min of live background counts are considered.

Fig. 11. Hourly gain values of background Detector 1 vs. time, which are used to correctly map gain variations.

ROIs

onto the background spectrum. Detector 8, not shown, had no

Appendix D. Gain Locking Systematics The gain locking of the digiBASE is excellent, but not perfect. It will be seen below that the effects of the observed tiny drifts in peak positions cause very small, gradual, fractional changes in the counting rates over the entire data taking period. This should have negligible effects on the fitted size of any steps in the counting rates. Typical changes in the fitted peak positions are a few hundredths of a spectral bin width (Fig. 12) with the exception of the higher energy 60Co and 22Na peaks which have overall (and nonlinear) drifts of 0.12 and 0.14 of a bin width, respectively, which are still small. The gain is being locked for only one ROI (peak) per detector; if there are slight nonlinear changes in gain across the spectrum, the higher peaks can drift slightly. The report files used to make the plots list the peak position to the nearest hundredth of a bin width, as can be seen from the quantization of the levels in the figure. The scatter of a few hundredths of a bin width from hour to hour, presumably due to the statistics in the peaks, is sufficient to support linear least square fits to the data for four of the peaks, from which we read off beginning and ending peak positions. For the worst-case upper 60Co and 22Na peaks, we easily extract the total drift by eye. The results are presented in Table 9. The fractional effects on the counting rates over the entire data taking period are in all cases less than 1.1× 10 4 . This has a completely negligible effect on the determination of ε, and we omit this systematic error from the analysis.

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Fig. 12. Peak locations as recorded by MAESTRO for: (a) 54Mn Det.2 (b) 54Mn Det.7 (c) 22 Na annih. (d) 22Na gamma (e) 60Co low (f) 60Co high. The red lines are linear fits to the data.

Table 9

Systematic Effects of Drifting Peak Location Radionuclide

54

Mn

Peak Energy

835 keV (Det. 2)

835 keV (Det. 7)

22

Na

511 keV

60

Co

1173 keV

1275 keV 1333 keV

Fractional

Hourly Counts

Fractional Change

Peak Shift

of Peak

in Counts

−2.4× 10 −5.6× 10

−3.5× 10

5

5

−2.43× 10

3.01× 107

−6.4× 10

6

2.53× 107

−2.4× 10

6

3.58× 107

5

2.25× 10 4 −1.8× 10 5

ROI

4

4.2× 106 1.36× 107 1.13× 107

−1.33× 10

5

−1.089× 10 4 −3.07× 10 5 −9.86× 10

5

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